find the area under the standard normal curve that lies between the following z-values. round the answers to four decimal places.
part: 0 / 2
part 1 of 2
(a) find the area under the standard normal curve that lies between z = -2.32 and z = -0.82.
the area between z = -2.32 and z = -0.82 is

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Accepted Answer

# Explanation:
## Step1: Recall the standard normal distribution properties
The area under the standard normal curve between two z - values $ z_1 $ and $ z_2 $ (where $ z_1<z_2 $) is given by $ P(z_1 < Z<z_2)=P(Z < z_2)-P(Z < z_1) $, where $ Z $ follows the standard normal distribution $ N(0, 1) $.

## Step2: Find $ P(Z < - 0.82) $ and $ P(Z < - 2.32) $
We can use the standard normal table (z - table) to find these probabilities.
- For $ z=-0.82 $: Looking up in the z - table, the row for $ - 0.8 $ and column for $ 0.02 $, we get $ P(Z < - 0.82)=0.2061 $.
- For $ z = - 2.32 $: Looking up in the z - table, the row for $ - 2.3 $ and column for $ 0.02 $, we get $ P(Z < - 2.32)=0.0102 $.

## Step3: Calculate the area between $ z=-2.32 $ and $ z = - 0.82 $
Using the formula $ P(-2.32<Z < - 0.82)=P(Z < - 0.82)-P(Z < - 2.32) $
Substitute the values we found: $ 0.2061 - 0.0102=0.1959 $

# Answer:
$ 0.1959 $

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QUESTION IMAGE

Question

Explanation:

Step1: Recall the standard normal distribution properties

Step2: Find \( P(Z < - 0.82) \) and \( P(Z < - 2.32) \)

Step3: Calculate the area between \( z=-2.32 \) and \( z = - 0.82 \)

Answer: